scholarly journals The accuracy of modeling of Gaussian stochastic process in some Orlicz spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 127-135
Author(s):  
YU. V. Kozachenko ◽  
Antonina Tegza ◽  
N. V.Troshki
Keyword(s):  
Stochastic Process ◽  
Orlicz Spaces ◽  
Model Parameters ◽  
Suitable Model ◽  
Gaussian Stochastic Process

The main purpose of this study is the construction of a model of a Gaussian stochastic process with given reliability and accuracy in some Orlicz spaces. In the paper, a suitable model is presented, conditions for the model parameters are derived, and some examples of their calculations are given.

scholarly journals Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão
Keyword(s):  
Stochastic Process ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Moving Average ◽  
Practical Importance ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Missing Observations ◽  
Data Set ◽  
The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

scholarly journals Simulation of thermal cycle aging process on fiber-reinforced polymers by extended finite element method

2017 ◽  
Vol 52 (14) ◽  
pp. 1947-1958 ◽  
Author(s):  
Sergio González ◽  
Gianluca Laera ◽  
Sotiris Koussios ◽  
Jaime Domínguez ◽  
Fernando A Lasagni
Keyword(s):  
Finite Element ◽  
Degradation Process ◽  
Damage Mechanism ◽  
Fiber Reinforced Polymers ◽  
Model Parameters ◽  
Suitable Model ◽  
Fiber Reinforced ◽  
Aging Effects ◽  
Extended Finite Element ◽  
Element Analysis

The simulation of long life behavior and environmental aging effects on composite materials are subjects of investigation for future aerospace applications (i.e. supersonic commercial aircrafts). Temperature variation in addition to matrix oxidation involves material degradation and loss of mechanical properties. Crack initiation and growth is the main damage mechanism. In this paper, an extended finite element analysis is proposed to simulate damage on carbon fiber reinforced polymer as a consequence of thermal fatigue between −50℃ and 150℃ under atmospheres with different oxygen content. The interphase effect on the degradation process is analyzed at a microscale level. Finally, results are correlated with the experimental data in terms of material stiffness and, hence, the most suitable model parameters are selected.

scholarly journals Robust Gaussian stochastic process emulation

2018 ◽  
Vol 46 (6A) ◽  
pp. 3038-3066 ◽  
Author(s):  
Mengyang Gu ◽  
Xiaojing Wang ◽  
James O. Berger
Keyword(s):  
Stochastic Process ◽  
Gaussian Stochastic Process

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

scholarly journals A New Flexible Version of the Lomax Distribution with Applications

2018 ◽  
Vol 7 (5) ◽  
pp. 120
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Estimation Method ◽  
Good Alternative ◽  
Model Parameters ◽  
Data Sets ◽  
Suitable Model ◽  
Lifetime Data ◽  
New Model ◽  
The Right ◽  
New Distribution ◽  
Better Than

A new version of the Lomax model is introduced andstudied. The major justification for the practicality of the new model isbased on the wider use of the Lomax model. We are also motivated tointroduce the new model since the density of the new distribution exhibitsvarious important shapes such as the unimodal, the right skewed and the leftskewed. The new model can be viewed as a mixture of the exponentiated Lomaxdistribution. It can also be considered as a suitable model for fitting thesymmetric, left skewed, right skewed, and unimodal data sets. The maximumlikelihood estimation method is used to estimate the model parameters. Weprove empirically the importance and flexibility of the new model inmodeling two types of aircraft windshield lifetime data sets. The proposedlifetime model is much better than gamma Lomax, exponentiated Lomax, Lomaxand beta Lomax models so the new distribution is a good alternative to thesemodels in modeling aircraft windshield data.

scholarly journals The maximum distribution of a Gaussian stochastic process indexed by a local field

1989 ◽  
Vol 46 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Steven N. Evans
Keyword(s):  
Stochastic Process ◽  
Vector Space ◽  
Compact Subset ◽  
Local Field ◽  
Asymptotic Expression ◽  
Independent Interest ◽  
Gaussian Stochastic Process ◽  
High Level

AbstractWe consider continuous Gaussian stochastic process indexed by a compact subset of a vector space over a local field. Under suitable conditions we obtain an asymptotic expression for the probability that such a process will exceed a high level. An important component in the proof of these results is a theorem of independent interest concerning the amount of ‘time’ which the process spends at high levels.

A Preliminary Theoretical Study of Arterial Pressure Perturbations Under Shock Acceleration

1989 ◽  
Vol 111 (3) ◽  
pp. 233-240 ◽  
Author(s):  
E. Belardinelli ◽  
M. Ursino ◽  
E. Iemmi
Keyword(s):  
Young Modulus ◽  
Qualitative Evaluation ◽  
The Body ◽  
Shock Acceleration ◽  
Model Parameters ◽  
Suitable Model ◽  
Mathematical Inquiry ◽  
The Common ◽  
Pressure Changes ◽  
Pressure Perturbations

The artero-venous system is often stressed by accelerative perturbation, not only during exceptional performances, but also in normal life. For example, when the body is subject to fast pressure changes, accelerative perturbations combined with a change in hydrostatic pressure could have severe effects on the circulation. In such cases a preliminary mathematical inquiry, whose results allow qualitative evaluation of the perturbation produced is useful. Pressure variations are studied in this work when the body is subjected both to rectilinear and rotational movements as well as posture change. The dominant modes of the hemodynamic oscillations are emphasized and the numerical simulation results presented. The artery model used for simulation is obviously simplified with respect to the anatomical structure of an artery. Nevertheless, behavior of the main arteries (like the common carotid and aorta) can be approximately described, choosing suitable model parameters. The frequency of blood oscillations strictly depends on the Young modulus of the arterial wall. This connection could be employed for new clinical tests on the state of the arteries.

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